Perpetual Futures for Stocks: The SpaceX Pre-IPO Market

Robert Shiller proposed perpetual futures in 1993 to create derivative markets for assets that are illiquid or whose price cannot be observed directly, such as single family homes, human capital, and the consumer price index. The crypto markets later built the instrument for a different reason and with a different funding rule. We give a single no arbitrage result that nests both designs: the perpetual price is the present value of a benchmark flow discounted at the funding rate, so the funding rule chooses both the benchmark and the discount. We give a random time change representation in which the price is the expected spot at the first event of a clock whose intensity is the funding rate, use it to show that stochastic volatility moves the basis only through the carry, so a volatility risk premium and not volatility itself can break the peg, read price discovery as the convergence of a Doob martingale driven by a stochastic approximation, and give a segmented market equilibrium that makes the pre listing premium structural rather than behavioural. The June 2026 SpaceX pre-IPO market is the first large scale realization of the idea for an equity claim, and we find that the perpetual consensus forecast the secondary clearing price more accurately than the bookbuilt offer. We close with other equity applications.